Toposes of connectivity spaces. Morita equivalences with topological spaces and partially ordered sets in the finite case

2018/03/06 by Dugowson, Stéphane
#Category Theory (math.CT) #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1803.02275

Abstract

This paper has two parts. First, we recall and detail the definition of the Grothendieck topos of a connectivity space, that is the topos of sheaves on such a space. In the second part, we prove that every finite connectivity space is Morita-equivalent to a finite topological space, and vice versa (we have given this proof in several, but we haven't yet shared this in writing).

Related

• The Topos Of A Connectivity Space
• Toposes over which essential implies locally connected
• Sheaves of ordered spaces and interval theories
• Sites and Grothendieck toposes: an introduction
• Denseness conditions, morphisms and equivalences of toposes